Methods of Randomization in Experimental Design

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.

Sir James Jeans has used his remarkable gifts of exposition to set out all that is relevant in the science of acoustics to the art of music. He offers a simple but precise account (illustrated with well-chosen photographs and diagrams) of the anatomical origin and workings of the human ear; the nature of sound vibrations; simple tones and complex sounds; the principles and operation of musical instruments; harmony and the musical scale; the effects of music on men and animals; and the practical problems of acoustical design. Scientists who appreciate music, musicians with an interest in science and laymen who care for both, will thoroughly enjoy this book.

More than sixty speculative art and design projects explore how art, food, and creative thinking can prepare us for future catastrophes.In the Age of the Anthropocene―a era characterized by human-caused climate disaster―catastrophes and dystopias loom. The Anthropocene Cookbook takes our planetary state of emergency as an opportunity to seize the moment to imagine constructive change and new ideas. How can we survive in an age of constant environmental crises? How can we thrive? The Anthropocene Cookbook answers these questions by presenting a series of investigative art and design projects that explore how art, food, and creative thinking can prepare us for future catastrophes. This cookbook of ideas rethinks our eating habits and traditions, challenges our food taboos, and proposes new recipes for humanity’s survival. These more than sixty projects propose new ways to think and make food, offering tools for creative action rather than traditional recipes. They imagine modifying the h

Clinics Collections: Depression draws from Elsevier's robust Clinics Review Articles database to provide multidisciplinary teams, including psychiatrists, general practitioners, and pediatricians, with practical clinical advice and insights on how telehealth can be implemented in individual specialties.Clinics Collections: Telehealth guides readers on how to apply current best practices in the implementation of telehealth to everyday practice to help overcome patient challenges and complications, keep up with new and advanced treatment methods, and improve patient outcomes.Areas of focus include implementation of telehealth in pediatric care, sleep medicine, gynecology and women's health, and telepsychiatry.Each article begins with keywords and key points for immediate access to the most critical information.Articles are presented in an easy-to-digest and concisely worded format.

Through a series of case studies this book demonstrates the wide-ranging impact of demographic dynamics on social, economic and political structures in the Graeco-Roman world. The individual case studies focus on fertility, mortality and migration and the roles they played in various aspects of ancient life. These studies - drawn from a range of populations in Athens and Attica, Rome and Italy, and Graeco-Roman Egypt - illustrate how new insights can be gained by applying demographic methods to familiar themes in ancient history. Methodological issues are addressed in a clear, straightforward manner with no assumption of prior technical knowledge, ensuring that the book is accessible to readers with no training in demography. The book marks an important step forward in ancient historical demography, affirming both the centrality of population studies in ancient history and the contribution that antiquity can make to population history in general.

Through a series of case studies this book demonstrates the wide-ranging impact of demographic dynamics on social, economic and political structures in the Graeco-Roman world. The individual case studies focus on fertility, mortality and migration and the roles they played in various aspects of ancient life. These studies - drawn from a range of populations in Athens and Attica, Rome and Italy, and Graeco-Roman Egypt - illustrate how new insights can be gained by applying demographic methods to familiar themes in ancient history. Methodological issues are addressed in a clear, straightforward manner with no assumption of prior technical knowledge, ensuring that the book is accessible to readers with no training in demography. The book marks an important step forward in ancient historical demography, affirming both the centrality of population studies in ancient history and the contribution that antiquity can make to population history in general.

A critique of concepts has been central to feminist scholarship since its inception. However, while gender scholars have identified the analytical gaps in existing social science concepts, few have systematically mapped out a gendered approach to issues in political analysis and theory development. This volume addresses this important gap in the literature by exploring the methodology of concept construction and critique, which is a crucial step to disciplined empirical analysis, research design, causal explanations, and testing hypotheses. Leading gender and politics scholars use a common framework to discuss methodological issues in some of the core concepts of feminist research in political science, including representation, democracy, welfare state governance, and political participation. This is an invaluable work for researchers and students in women's studies and political science.

A critique of concepts has been central to feminist scholarship since its inception. However, while gender scholars have identified the analytical gaps in existing social science concepts, few have systematically mapped out a gendered approach to issues in political analysis and theory development. This volume addresses this important gap in the literature by exploring the methodology of concept construction and critique, which is a crucial step to disciplined empirical analysis, research design, causal explanations, and testing hypotheses. Leading gender and politics scholars use a common framework to discuss methodological issues in some of the core concepts of feminist research in political science, including representation, democracy, welfare state governance, and political participation. This is an invaluable work for researchers and students in women's studies and political science.

The aim of this study is to examine the speeches given to leading characters in the Books of Chronicles, including those which formed the basis of Gerhard von Rad's book The Levitical Sermon in the Books of Chronicles. These are compared with similar material in the Books of Ezra and Nehemiah and in the post-exilic prophets. It is Dr Mason's contention that recurring themes and homiletical devices suggest that these 'addresses' (while not to be classified as 'Sermons') do reveal something of the exegetical and teaching methods employed in the Second Temple period, which are here echoed. By studying the contents and aims of this preaching, the author tries to clarify the process by which pre-exilic Davidic Yahwism became the living faith of the post-exilic community in the challenging circumstances of the Persian and Greek periods through the careful reinterpretation of earlier scriptural material.

The aim of this study is to examine the speeches given to leading characters in the Books of Chronicles, including those which formed the basis of Gerhard von Rad's book The Levitical Sermon in the Books of Chronicles. These are compared with similar material in the Books of Ezra and Nehemiah and in the post-exilic prophets. It is Dr Mason's contention that recurring themes and homiletical devices suggest that these 'addresses' (while not to be classified as 'Sermons') do reveal something of the exegetical and teaching methods employed in the Second Temple period, which are here echoed. By studying the contents and aims of this preaching, the author tries to clarify the process by which pre-exilic Davidic Yahwism became the living faith of the post-exilic community in the challenging circumstances of the Persian and Greek periods through the careful reinterpretation of earlier scriptural material.

The authors of this tract present a treatment of generalised Clifford parallelism within the framework of complex projective geometry. After a brief survey of the necessary preliminary material, the principal properties of systems of mutually Clifford parallel spaces are developed, centred round discussion of an extended form of the Hurwitz - Radon matrix equations. Later chapters deal with methods for the construction and representation of such systems. Much of the work in the tract is previously unpublished. Some emphasis has been placed throughout on special cases (particularly on the exceptionally interesting parallelisms that exist in spaces of seven and fifteen dimensions). Numerous exercises give the reader a clear insight into the fresh ideas presented. The tract will be of interest to advanced undergraduates and graduates with special interests in algebraic and projective geometry or in the geometry of matrices.

By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.

This wide-ranging comparative account of the legal regimes for controlling administrative power in England, the USA and Australia argues that differences and similarities between control regimes may be partly explained by the constitutional structures of the systems of government in which they are embedded. It applies social-scientific and historical methods to the comparative study of law and legal systems in a novel and innovative way, and combines accounts of long-term and large-scale patterns of power distribution with detailed analysis of features of administrative law and the administrative justice systems of three jurisdictions. It also proposes a new method of analysing systems of government based on two different models of the distribution of public power (diffusion and concentration), a model which proves more illuminating than traditional separation-of-powers analysis.

This wide-ranging comparative account of the legal regimes for controlling administrative power in England, the USA and Australia argues that differences and similarities between control regimes may be partly explained by the constitutional structures of the systems of government in which they are embedded. It applies social-scientific and historical methods to the comparative study of law and legal systems in a novel and innovative way, and combines accounts of long-term and large-scale patterns of power distribution with detailed analysis of features of administrative law and the administrative justice systems of three jurisdictions. It also proposes a new method of analysing systems of government based on two different models of the distribution of public power (diffusion and concentration), a model which proves more illuminating than traditional separation-of-powers analysis.

Using classical and quantum methods with a strong emphasis on symmetry principles, this book, a reissue of the 2004 second edition, develops the theory of a variety of optical activity and related phenomena from the perspective of molecular scattering of polarised light. In addition to the traditional topic of optical rotation and circular dichroism in the visible and near-ultraviolet associated with electronic transitions, the newer topic of optical activity associated with vibrational transitions, which may be studied using both infrared and Raman techniques, is also treated. Ranging from the physics of elementary particles to the structure of viruses, the subject matter of the book reflects the importance of optical activity and chirality in much of modern science and will be of interest to a wide range of physical and life scientists.

This reference book provides updated information on the production and industrial significance of bacterial cellulose. Bacterial cellulose is a natural fiber produced by certain microbes, mainly bacteria which belong to the Acetobacter genera. The book discusses its applications in different industrial sectors like food, pharmaceutical, energy and wastewater treatment. It covers the production of cellulose from conventional and renewable feedstocks. It includes topics like downstream processing, characterization, and chemical modification of bacterial cellulose. Key features- Addresses the challenge on the production technologies of bacterial cellulose up to pilot-scale Discusses cost-effective, green processes using agri-processing residues and medium formulation Includes efficient preparation of nano-composite using in vitro and in vivo methods Provides latest applications of bacterial cellulose in food and pharmaceuticals fields Reviews the production of bacterial fro

Observational cosmology, with the help of large telescopes, combined with the capabilities of the Hubble Space Telescope and other space missions, allow astronomers to directly observe galaxy assembly over cosmic time. These developments demand that scientists are trained in the methods suited to the study of distant galaxies. This volume contains the lectures delivered at the XI Canary Islands Winter School of Astrophysics, reviewing both scientific results and the main questions in the field. It covers the study of normal galaxies, distant galaxies, and studies based on far-infrared diagnostics, it reviews quasar absorption lines, and the properties of nearby galaxies. Each chapter is written by a world expert in the field, making the book an essential reference for all astronomers working in the field of high-redshift galaxies.

Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.

Observational cosmology, with the help of large telescopes, combined with the capabilities of the Hubble Space Telescope and other space missions, allow astronomers to directly observe galaxy assembly over cosmic time. These developments demand that scientists are trained in the methods suited to the study of distant galaxies. This volume contains the lectures delivered at the XI Canary Islands Winter School of Astrophysics, reviewing both scientific results and the main questions in the field. It covers the study of normal galaxies, distant galaxies, and studies based on far-infrared diagnostics, it reviews quasar absorption lines, and the properties of nearby galaxies. Each chapter is written by a world expert in the field, making the book an essential reference for all astronomers working in the field of high-redshift galaxies.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

How would feminist perspectives and analytical methods change the interpretation of employment discrimination law? Would the conscious use of feminist perspectives make a difference? This volume shows the difference feminist analysis can make to the interpretation of employment discrimination statutes. This book brings together a group of scholars and lawyers to rewrite fifteen employment discrimination decisions in which a feminist analysis would have changed the outcome or the courts' reasoning. It demonstrates that use of feminist perspectives and methodologies, if adopted by the courts, would have made a significant difference in employment discrimination law, leading to a fairer and more egalitarian workplace, and a more prosperous society.

How would feminist perspectives and analytical methods change the interpretation of employment discrimination law? Would the conscious use of feminist perspectives make a difference? This volume shows the difference feminist analysis can make to the interpretation of employment discrimination statutes. This book brings together a group of scholars and lawyers to rewrite fifteen employment discrimination decisions in which a feminist analysis would have changed the outcome or the courts' reasoning. It demonstrates that use of feminist perspectives and methodologies, if adopted by the courts, would have made a significant difference in employment discrimination law, leading to a fairer and more egalitarian workplace, and a more prosperous society.

In this radically new approach to morphological typology, the authors set out new and explicit methods for the typological classification of languages. Drawing on evidence from a diverse range of languages including Chinantec, Dakota, French, Fur, Icelandic, Ngiti and Sanskrit, the authors propose innovative ways of measuring inflectional complexity. Designed to engage graduate students and academic researchers, the book presents opportunities for further investigation. The authors' data sets and the computational tool that they constructed for their analysis are available online, allowing readers to employ them in their own research. Readers can access the online computational tool through www.cambridge.org/stump_finkel.

In this radically new approach to morphological typology, the authors set out new and explicit methods for the typological classification of languages. Drawing on evidence from a diverse range of languages including Chinantec, Dakota, French, Fur, Icelandic, Ngiti and Sanskrit, the authors propose innovative ways of measuring inflectional complexity. Designed to engage graduate students and academic researchers, the book presents opportunities for further investigation. The authors' data sets and the computational tool that they constructed for their analysis are available online, allowing readers to employ them in their own research. Readers can access the online computational tool through www.cambridge.org/stump_finkel.

An introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations.This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents “should” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.Features:Each chapter begins with a motivating example that can be run as an experiment and ends with a discussion of the beh

The thalamus is a key structure in the mammalian brain, providing a hub for communication within and across distributed forebrain networks. Research in this area has undergone a revolution in the last decade, with findings that suggest an expanded role for the thalamus in sensory processing, motor control, arousal regulation, and cognition. Moving beyond previous studies of anatomy and cell neurochemistry, scientists have expanded into investigations of cognitive function, and harness new methods and theories of neural computation. This book provides a survey of topics at the cutting edge of this field, covering basic anatomy, evolution, development, physiology and computation. It is also the first book to combine these disciplines in one place, highlighting the interdisciplinary nature of thalamus research, and will be an essential resource for students and experts in biology, medicine and computer science.

The modernist period witnessed attempts to explain religious experience in non-religious terms. Such novelists as Henry James, Marcel Proust, James Joyce, Virginia Woolf and Franz Kafka found methods to describe through fiction the sorts of experiences that had traditionally been the domain of religious mystics and believers. In Religious Experience and the Modernist Novel, Pericles Lewis considers the development of modernism in the novel in relation to changing attitudes to religion. Through comparisons of major novelists with sociologists and psychologists from the same period, Lewis identifies the unique ways that literature addressed the changing spiritual situation of the early twentieth century. He challenges accounts that assume secularisation as the main narrative for understanding twentieth-century literature. Lewis explores the experiments that modernists undertook in order to invoke the sacred without directly naming it, resulting in a compelling study for readers of twenti

R. S. Silver began to criticise convention teaching ideas when, as an employer of graduate engineers, he saw how unimaginative their training sometimes made them. In industry, thermodynamic problems are not presented in pure 'textbook' style: they arise casually, in real, complex situations, and newly graduated engineers take some time to outgrow the resulting confusion. Originally published in 1971, this book offers a different approach to the standard industry textbook. Throughout the book, Silver considers real processes, including frictional dissipation: conventional introductions to thermodynamics are limited to idealized reversible processes. Another major difference is that he avoids the unusual procedure of hiding important difficulties in thermodynamic concepts under premature definitions. This book will be of value to anyone with an interest in the practical application of thermodynamics, and the development of pedagogical methods in relation to it.

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

In vivo magnetic resonance spectrosopy (MRS) is increasingly being used in the clinical setting, particularly for neurological disorders. Clinical MR Spectroscopy – Techniques and Applications explains both the underlying physical principles of MRS and provides a perceptive review of clinical MRS applications. Topics covered include an introduction to MRS physics, information content of spectra from different organ systems, spectral analysis methods, recommended protocols and localization techniques, and normal age- and region-related spectral variations in the brain. Clinical applications in the brain are discussed for brain tumors, hypoxic and ischemic injury, infectious, inflammatory and demyelinating diseases, epilepsy, neurodegenerative disorders, trauma and metabolic diseases. Outside of the brain, techniques and applications are discussed for MRS in the musculosketal system, breast and prostate. Written by leading MRS experts, this is an invaluable guide for anyone interested in

This Companion, first published in 2000, provides a comprehensive view of Beethoven and his work. The first part of the book presents the composer as a private individual, as a professional, and at the work-place, discussing biographical problems, Beethoven's professional activities when not composing and his methods as a composer. In the heart of the book, individual chapters are devoted to all the major genres cultivated by Beethoven and to the elements of style and structure that cross all genres. The book concludes by looking at the ways that Beethoven and his music have been interpreted by performers, writers on music, and in the arts, literature, and philosophy. The essays in this volume, written by leading Beethoven specialists, maintain traditional emphases in Beethoven studies while incorporating other developments in musicology and theory.

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of th

The New English Bible has benefited not only from advances in the understanding of ancient language and discoveries of new manuscripts and methods, but also from the recent growth in knowledge of the social and political history of the biblical period and the development of new ways of evaluating prehistory. In Understanding the Old Testament the essentials of the background and context of the Old Testament and Apocrypha are set out as concisely as possible to enable the reader to understand the meaning and significance of much that can only be appreciated fully with the help of this background material. The geographical setting, the prehistory, the social and political history, as well as the nature of the ideas which grew in this context are all described. The literary point i=of view is on the Old Testament and Apocrypha presented in the companion volume, The Making of the Old Testament.

This volume is the first reader on video games and learning of its kind. Covering game design, game culture and games as twenty-first-century pedagogy, it demonstrates the depth and breadth of scholarship on games and learning to date. The chapters represent some of the most influential thinkers, designers and writers in the emerging field of games and learning - including James Paul Gee, Soren Johnson, Eric Klopfer, Colleen Macklin, Thomas Malaby, Bonnie Nardi, David Sirlin and others. Together, their work functions both as an excellent introduction to the field of games and learning and as a powerful argument for the use of games in formal and informal learning environments in a digital age.

This volume is the first reader on video games and learning of its kind. Covering game design, game culture and games as twenty-first-century pedagogy, it demonstrates the depth and breadth of scholarship on games and learning to date. The chapters represent some of the most influential thinkers, designers and writers in the emerging field of games and learning - including James Paul Gee, Soren Johnson, Eric Klopfer, Colleen Macklin, Thomas Malaby, Bonnie Nardi, David Sirlin and others. Together, their work functions both as an excellent introduction to the field of games and learning and as a powerful argument for the use of games in formal and informal learning environments in a digital age.

Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.

The study of permutation patterns is a thriving area of combinatorics that relates to many other areas of mathematics, including graph theory, enumerative combinatorics, model theory, the theory of automata and languages, and bioinformatics. Arising from the Fifth International Conference on Permutation Patterns, held in St Andrews in June 2007, this volume contains a mixture of survey and research articles by leading experts, and includes the two invited speakers, Martin Klazar and Mike Atkinson. Together, the collected articles cover all the significant strands of current research: structural methods and simple patterns, generalisations of patterns, various enumerative aspects, machines and networks, packing, and more. Specialists in this area and other researchers in combinatorics and related fields will find much of interest in this book. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertati

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geo